Question

A and B invested rs. 4800 and rs. 7200 respectively. B invested for two more months than A. If total annual profit is RS. 5750 and the share of A in profit is RS. 2000, then for how many months did B invest?

Answer 1

B invested for 10 months

Step-by-step explanation:

Consider A invested for x months,

So, the time for which B invested = (x+2) months,

Given,

A'investment = 4800 rupees

B'investment = 7200 rupees,

Since, if rate of interest is same, the profit is jointly proportional to investment and time,

Thus, the ratio of profits of A and B

= 4800(x) : 7200(x+2)

= 2x : 3(x+2)

∵ A's share = rs 2000, total profit = rs 5750 ⇒ B's share = 5750 - 2000 = 3750

$\implies \frac{2x}{3(x+2)}=\frac{2000}{3750}$

$\frac{2x}{3x+6}=\frac{8}{15}$

By cross multiplication,

30x = 24x + 48

30x - 24x = 48

6x = 48

⇒ x = $\frac{48}{6}$ = 8,

Hence, the time for which B invested = 8 + 2 = 10 months.

#Learn more:

A, B and C started a business in which A contributed Rs 30,000. Out of the total profit of Rs 7200, A got Rs 1920 and C got Rs 2880, find the capital invested by B?

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